When I lived in Europe for a couple months, my first time there I grocery shopped like an American - filled up an entire cart with a week or two worth of groceries and then everyone stared at me when I checked out.
It's absolutely true that Europeans who live in walkable cities go to the market to pick up groceries a few times a week. Americans simply do not, with very few exceptions.
The grocery store density is much higher though. There were at least 2 grocery stores within a 5 minute walk from anywhere I've stayed in a city core in Europe. At least a dozen within 15 minutes.
It's simply a difference in culture. There are plenty of places in the US where you could drive to half a dozen grocery stores within 15 minutes but people simply don't do so. The store sizes reflect this cultural difference too. The average grocery store in the US seems to be 4-6x larger than those in Europe.
Your mileage varies, I guess. I used to live with easy walking distance of an upscale supermarket, but yet I did most of my shopping by driving to a different one farther away. Buying groceries with a car is simply more convenient.
Even after I moved out of that neighborhood, it wasn't unusual for me to stop at the grocery store every afternoon on my drive home.
Is that really how the average American shops though? The majority of shoppers these days are in the self checkout or "15 items or less" lines with only a single basket of stuff, at least in the stores I frequent. Granted, I'm close to a city center but the store I go to is not very walkable